A gamma-minimax result in credibility theory

A generalization of the credibility theory obtained by using the weighted balanced loss function

“…The weighted factor is referred as the credibility factor. Some historical references on this topic are Whitney (1918), Mowbray (1914), Bailey (1945), Bühlmann (1967), Kahn (1975), Gerber and Arbor (1980), Eichenauer et al (1988), Heilmann (1989), Goovaerts et al (1990) and Herzog (1996). For a recent revision of the credibility theory see Makov (1999, 2000), Promislow and Young (2000), Young (2000) and Gómez et al (2006).…”

The Esscher premium principle in risk theory: a Bayesian sensitivity study

“…Papers using Poisson-Gamma models abound in risk theory literature (see e.g. Eichenauer et al, 1988;Klugman, 1992;Freifelder, 1974, and references therein). From (1), the true individual premium is given by P (θ) = θ e α .…”

“…The actuary may have difficulty in providing suitable information about a uniquely specified prior of θ , perhaps because of insufficient information to identify a single prior (Eichenauer et al, 1988). It is then natural to question the robustness of the analysis for this specification.…”

“…The use of standard Bayesian analysis in risk theory has been considered in several actuarial applications (Makov et al, 1996;Eichenauer et al, 1988;Heilmann, 1989;Klugman et al, 1998, among others). When using Bayesian analysis to model insurance loss, the practitioner usually chooses a prior distribution (structure function in risk theory).…”

Loss prediction based on run-off triangles

“…For a decision theoretic approach to parameter estimation in certain credibility models, seeEichenauer et al (1988) andSchmidt (2000).…”